IEEE Computational Intelligence Magazine - August 2021 - 90

that the accuracy of these five methods
is higher than the KNN, LR, SVM, NB,
and MLP methods using raw signals
amplitude. Among these five methods
using the manually crafted features, the
IMDE method achieves the best results
(the maximal and average diagnosis
accuracy are 91.11%) on NCEPU, the
MMSDE method achieves
the best
results (the maximal and average diagnosis
accuracy are 92.67%) on CWRU,
and the FDF method achieves the best
results (the maximal and average diagnosis
accuracy are 97.22%) on XJTU.
The results show that it is necessary to
extract a set of effective features according
to the datasets to perform fault
diagnosis because the performance of
the manually extracted features varies
with datasets. Compared with these
methods, MFCGPE achieves much better
performance by automatically constructed
multi-view high-level features
and building an ensemble for fault diagnosis.
The adaptability of MFCGPE is
much higher than these five methods as
it achieves the best results on all the
three datasets.
Rows 11 to 13 of Table VII are the
classification results of the GP based
comparison methods for constructing a
single feature, i.e., GPS-TDF, GPS-FDF,
and GPS-TFDF. Among these methods,
GPS-TFDF achieves the best results on
all three datasets by obtaining an average
accuracy of 90.73% on NCEPU,
90.17% on CWRU and 96.67% on
XJTU. Compared with these three
methods, MFCGPE achieves better and
stable classification performance. The
results show that only constructing one
high-level feature may not be effective
for multi-class fault diagnosis. Compared
with these methods, MFCGPE is
able to construct a flexible number of
effective features from every single view
for fault diagnosis.
Rows 14 to 16 of Table VII are the
classification results of the GP based
comparison methods that construct
multiple features for fault diagnosis, i.e.,
GPM-TDF, GPM-FDF, and GPMTFDF.
Among these three methods,
GPM-TFDF achieves better results on
all three datasets. Specifically, GPMTFDF
achieves an average diagnosis
accuracy of 94.56%, 96.16%, and
98.21% on NCEPU, CWRU and
XJTU, respectively. Compared with the
GPS-based methods, the GPM-based
methods achieve higher average accuracy
and smaller standard deviation values.
These results indicate that using multiple
constructed high-level features is
more effective than using a single constructed
high-level feature to improve
diagnosis performance. Compared with
these three methods, MFCGPE achieves
better performance on the three datasets.
MFCGPE builds an effective ensemble
using the features constructed from
multiple views, which allows it to obtain
higher generalization performance than
these methods using a single classifier.
Rows 17 to 19 of Table VII are the
classification results of the ensemble
diagnosis methods, i.e., OFE, GSE, and
GPME. It can be found that on the
NCEPU, CWRU, and XJTU datasets,
the diagnostic performance of OFE,
GPSE, and GPME is ranked the third,
the second, and the first, respectively.
Compared with these three methods,
MFCGPE achieves higher average accuracy
and smaller standard deviation values.
The reason is that MFCGPE has a new
program structure, function set, terminal
set, and fitness function, which allow it to
construct more discriminative features
and build a more effective ensemble to
obtain better diagnosis accuracy.
Row 20 and Row 21 of Table VII
lists the classification results and the significance
test results of the MFCGPE
approach, respectively. On the NCEPU,
CWRU, and XJTU dataset, MFCGPE
achieves the maximal accuracy of 100%
and the average accuracy of above 99%.
The results of the significance tests
show that the diagnosis performance of
MFCGPE is significantly better than
the 19 comparison methods on the
three datasets.
In summary, the results show that
MFCGPE is able to achieve excellent
fault diagnosis performance on three
datasets with a small number of training
samples. MFCGPE can adaptively construct
a flexible number of features for
fault diagnosis, which can not only
90 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | AUGUST 2021
achieve a comprehensive description of
the raw signal but also avoid redundancy
and information interference. The fitness
function based on accuracy and distance
enables MFCGPE to construct new
effective features that achieve a small
intra-class distance and a large inter-class
distance of the training samples, which
can improve the generalization performance
on the unseen test set. MFCGPE
constructs multiple high-level features
from different views, individually, and
constructs an effective ensemble based
on these constructed features through
the majority voting, which further
improves the effectiveness of the diagnostic
approach and avoids the overfitting
issue caused by using a small
number of training samples. Thus, MFCGPE
is a practical and promising
approach to engineering applications.
VI. Further Analysis
This section further analyses the evolved
GP tree/models, the features constructed
by GP from different views, and the
constructed ensemble to provide insights
into why the new approach is effective.
A. Example Trees/Models
Figure 12 shows the best trees/models
evolved by MFCGPE from the three
different views on the NCEPU dataset,
where the white oval nodes are the feature
combination operators, the white
circle nodes are the feature construction
operators, and the orange, blue, and pink
rectangle nodes are the features of View1,
View2, and View3, respectively.
As it can be seen from Figure 12, for
View1, six distinguished features among
the input 16 features are selected to
construct four high-level features. For
View2, six distinguished features among
the 13 input features are selected to
construct four high-level features. For
View3, five distinguished features among
the 29 input features are selected to
construct three high-level features. This
indicates that MFCGPE can automatically
select the useful features and determine
the number of constructed
features, which avoid information interference
and feature redundancy. The
depths of the trees evolved from View1,
IEEE Computational Intelligence Magazine - August 2021

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